A note on the definability of genus for Zariski geometries
Logic
2025-05-23 v2 Algebraic Geometry
Abstract
In this work we propose a notion of genus in the context of Zariski geometries and we obtain natural generalizations of the Riemann--Hurwitz Theorem and the Hurwitz Theorem in the context of very ample Zariski geometries. As a corollary, we show that such notion of genus cannot be first-order definable in the full language of a Zariski geometry.
Cite
@article{arxiv.2110.02218,
title = {A note on the definability of genus for Zariski geometries},
author = {Darío García and Pedro Rizzo and Joel Torres del Valle},
journal= {arXiv preprint arXiv:2110.02218},
year = {2025}
}
Comments
The paper contains a fault that can't be repaired